06/02/08 tough puzzle from sudoku.com.au

Today's puzzle needs a single 3sets-deep elimination. Beginners can profitably study this one.

Want to see the whole thing? A complete proof
Just stuck somewhere and willing to have still work to do ? Short hints for a proof
Studied enough forbidding chains to appreciate this Forbidding-chain-like proof ?

A complete proof

1) First eliminations : d2=7%row, c3=1%col, h9=7%block lead to 26 filled cells.

2)
Look at only possibles d5=4,h5=4 in their row. Whether d5=4 (in which case b7=4%row) or h5=4 (in which case b5=9%row), in both cases, we have no more {b7=9}.
Now easy fillings up to 81 filled cells. (If needed, f7=9%row, e2=9%block, f2=1%row, i6=9%col, i2=4%col, h3=9%block, i1=5%block, i9=8%cell, g1=2%row, h7=5%block, g7=1%cell, i4=1%block, g3=6%block, b5=9%row, i7=2%block, a8=9%row, b8=2%row, b4=5%col, b1=7%col, b3=3%block, b6=8%cell, b7=4%cell, a3=4%block, a1=8%block, a9=6%cell, c7=8%cell, d7=6%cell, e1=6%row, c6=6%row, f4=6%block, f5=2%block, d5=5%block, h5=4%row, e4=3%cell, f9=3%row, d1=3%col, c8=7%block, c9=5%col, e8=5%col, f8=8%cell, d3=8%row, d8=1%block, e6=1%block, d6=4%row, f3=5%cell, g5=7%row, a4=7%row, g4=8%cell, g2=3%col, a6=2%block, h2=8%col, h4=2%row, e9=4%row, c5=3%cell, h6=3%block)

Short hints for a proof

can you see the heptagon ?


1) easy to 26 filled.
2) with 4s in row 5, eliminate b7=9. Then easy to the end.

Total sets used :3, max depth :3.

Forbidding-chain-like proof

can you see the heptagon ?


around 26 filled
(b7=4)==(d7=4)--(d5=4)==(h5=4)--(h5=9)==(b5=9) forbids {b7=9}

That's all for today, folks...